LeetCode 62. Unique Paths 题解

题目描述：

62. Unique Paths

 

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A robot is located at the top-left corner of a m x n grid (marked 'Start' in the diagram below).

The robot can only move either down or right at any point in time. The robot is trying to reach the bottom-right corner of the grid (marked 'Finish' in the diagram below).

How many possible unique paths are there?

Above is a 3 x 7 grid. How many possible unique paths are there?

Note: m and n will be at most 100.

解题思路：

首先到达一个结点(x,y)(x>1.y>1)，有两种方法，即从(x-1,y),(x,y-1)，所以到(x,y)的路径数即为到(x-1,y)和(x,y-1)之和。搜索过程中，将已经走过的点的路径数记录下来，避免重复计算，从而提高运算效率。

代码展示：

//代码一
// 复杂度 O(n*n)   
class Solution {
public:
    int uniquePaths(int m, int n) {
        res = vector >(m,vector(n,0));
        res[0][0]=1;
        return dfs(m-1,n-1);
    }
private:
    //res 已搜索过的结点的路径数
    vector > res;
    int dfs(int x,int y)
    {
        if(x<0||y<0) return 0;
        if(x==0&&y==0) return 1;
        //如果未搜索过点x，y
        if(!res[x][y]) 
        {
            res[x][y]=dfs(x-1,y)+dfs(x,y-1);
            return res[x][y];
        }
        //若已求出到该点路径数，直接返回
        else return res[x][y];
        
    }
    
};